Demonstrate that here exist two positive integers which diff

Demonstrate that here exist two positive integers which differ by ten whose sum is one Million. Give both an existence proof and a constructive solution.

Solution

x-y=10

x+y=1000000

Existence proof

We have two non parallel lines in xy plane which must intersect at a point. That point of intersection gives us solution to this problem

Constructive solution

Adding the two equations gives

2x=1000010

x=500005

y=499995